1. Technical Field
The invention relates generally to communication systems; and, more particularly, it relates to system and method that are operable to perform an efficient approximately of decision metrics used in bit-soft decisions.
2. Related Art
Communication systems transmit digital data through imperfect communication channels. These symbols may undergo some undesirable corruption due to the imperfection of the communication channel. One effort to try to avoid such situations is focused on performing forward error correction (FEC) coding. However, there is typically some difficulty in extracting the information contained within these symbols after they have been undesirably altered within the communication channel. There exist some methods that seek to curb the effect that the communication channel has had on the data; one such method includes employing using Decision Feedback Equalizers (DFEs). However, even after the incoming signal has been equalized, the extraction of the data, that has undergone some alteration due to the channel effects, is still a probabilistic determination.
Many communication systems, particularly in a receiver, need to perform the analog to digital transformation of an incoming signal. In doing so, there is oftentimes an uncertainty in whether a sample of the incoming analog signal is properly transformed into a 1 or a 0 in the digital realm; for example, there is not a 100% certainty that an incoming signal is actually a 1 or actually a 0—there is some probability associated with the decision. In higher-level encoding/decoding systems, e.g., QPSK/4 QAM, 16 QAM, 64 QAM, 256 QAM, 1024 QAM etc., there are several bits per symbol that need to be transformed to either a 1 or a 0. In 16 QAM applications, a receiver extracts 4 bits of data from each symbol. In the QAM modulation scheme, each symbol includes an in-phase component and a quadrature component. For the 16 QAM modulation type, the decision block maps the in-phase and quadrature components contained in the symbol to a 16 QAM constellation and decides the values of the four bits that are carried by the symbol.
The decisions made in extracting bits from a particular symbol are referred to as “bit-soft decisions.” Bit-soft decisions not only map the symbol into bits but also produce a decision metric/branch metric related to the probability that the decision was correct based upon how well the symbol maps into the constellation. The terminology of “branch metric” is often used interchangeably with “decision metric,” and this convention will be followed in this document. The decoder operates based on the premise that there are only a finite number of possible states of the encoder and that given a certain number of consecutive states, the input bit may be predicted that would have caused a particular state transition. The decoder generates a “branch metric” (or “decision metric”) for each of the possible “state transitions” from one state to another. The coding method maintains a “decision metric” associated with every state which is the sum of the metric at its predecessor state and the metric associated with the branch that caused the state transition. This metric may be termed the cumulative metric, accumulated metric, or path metric, and the decoder generates the cumulative metric for all of the states. The different states and the transition from one state to another can be represented in a diagram, namely, a trellis diagram. For various possible allowable state transition sequences through the trellis (the allowable paths through the trellis), the decision metric associated with the sequence of branches of the trellis diagram are summed together, and the smallest sum is selected as the actual state transition and enables the identification of the best estimate of the decoded data. It is noted that with a sign change on each decision metric, the largest sum identifies the best path.
Prior art approaches to calculate decision metrics/branch metrics used in decoding systems typically are either very computationally intensive or deviate noticeably from the optimal metric. The computational intensiveness of the prior art approaches prohibits their implementation into many applications, particularly those that have relatively tight real estate and power consumption budgets. Again, these branch metrics are used to determine whether the mapping of a sample should be to that of a value of 1 or a value of 0. Many higher order coding schemes employ mapping of symbols into a constellation. In such situations, the various bits contained in the symbol, e.g., least significant bit (LSB), . . . most significant bit (MSB), etc. may be considered separately. For example, in the 16 QAM scheme, the in-phase component carries two bits while the quadrature phase component carries two bits. By considering separately each of the bits of the in-phase and quadrature components, the decision metrics may be employed in deciding whether the particular bit is a 1 or a 0, in making these bit-soft decisions.
One prior art approach is to employ the maximum a priori (MAP) approach, in which a probability of the source symbol is computed, based on information relating to the received, distorted symbol sequence. The bit-soft decision output of the MAP approach is termed a log-likelihood ratio (LLR) that is the logarithmic ratio of the probability of receiving a 1 divided by the probability of receiving a 0; these probabilities of determining the receipt of either a 1 or a 0 are often performed using Bayes Rule to the problem to determine the probability to reach a certain encoder state after receipt of a certain number of symbols and the probability to get from one encoder state to another with the received symbol sequence.
This is where the branch metrics come in; the branch metrics may be viewed as being the probabilities of the transitions from one encoder state to another. The branch metrics are a function of the received symbols and the model of the channel over which the symbols have been communicated. To illustrate the complexity of the prior art approach to calculating the decision metrics/branch metrics (that often involves the calculation of the LLR), a 16 QAM example is illustrated as shown below. One rail, containing 2 bits and 4 levels, is examined. The received voltage on the rail is Vrec. The 4 possible transmit levels are: constpa, constpb, constpc, and constpd. In the following equations, the levels constpta and constptb correspond to an MSB value of 0, and the variables constptc and constptd correspond to an MSB value of 1. To begin with, the log-likelihood function of a simple constellation point is as follows:−ln(e−(Vrec−constpta)2/2σ2)
Then, the log-likelihood function for MSB=0 is as follows:−ln(e−(Vrec−constpta)2/2σ2+e−(Vrec−constptb)2/2σ2)
A prior art method of calculating the log likelihood ratio of an optimal bit-soft decision (ODM) for the MSB is as shown below:ODM={−ln(e−(Vrec−constpta)2/2σ2+e−(Vrec−constptb)2/2σ2)}−{−ln(e−(Vrec−constptc)2/2σ2+e−(Vrec−constptd)2/2σ2)}
The ODM shown above, which is the LLR of the MSB bit-soft decision, is the optimal decision metric for 16 QAM, one rail, for the most significant bit (MSB). Clearly, the LLR may be taken as a logarithm of a ratio or a difference of logarithms; the difference is shown above. The implementation of such non-linear equations can be very complex. To calculate these decision metrics accurately using the above-described methods is typically very difficult (theoretically) and is even more difficult to apply. Therefore, these decision metrics are simply not employed in most communication systems.
Further limitations and disadvantages of conventional and traditional systems will become apparent to one of skill in the art through comparison of such systems with the invention as set forth in the remainder of the present application with reference to the drawings.